Subgroups — #2263×D₈₉ #36712558

Order 22784.

502 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022567	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022566	C₂	1	2	yes	maximal, complemented
5	#26022565	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022564	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022563	C₂	1	2	yes	maximal, complemented
8	SD₆₄×D₈₉	C₂	1	2	yes	maximal, complemented
9	D₃₂×D₈₉	C₂	1	2	yes	maximal, complemented
10	M₆₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2263	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₈₉	—	2	1	no	—
13	C₂×D₈×D₈₉	—	2	1	no	—
14	#19152031	C₂²	1	1	yes	characteristic, complemented
15	#19152030	C₂²	1	1	yes	characteristic, complemented
16	#19152029	—	2	1	no	—
17	#19152028	—	2	1	no	—
18	#19152027	C₂²	1	1	yes	characteristic, complemented
19	Q₃₂×D₈₉	C₂²	1	1	yes	characteristic, complemented
20	SD₃₂×D₈₉	—	2	1	no	—
21	C₂×D₁₄₂₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×#15667953	—	2	1	no	—
23	D₁₆×D₈₉	—	2	1	no	—
24	D₁₆×D₈₉	—	2	1	no	—
25	D₁₆×D₈₉	C₂²	1	2	yes	—
26	D₁₆×D₈₉	C₂²	1	2	yes	complemented
27	D₁₆×D₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
29	#19151437	C₂²	1	2	yes	complemented
30	#19151436	C₂²	1	2	yes	complemented
31	#19151435	C₂²	1	2	yes	complemented
32	D₂₈₄₈	C₂²	1	2	yes	complemented
33	#19151433	C₂²	1	2	yes	complemented
34	#19151433	C₂²	1	2	yes	complemented
35	#19151432	C₂²	1	1	yes	characteristic, complemented
36	#19151431	C₂²	1	2	yes	complemented
37	C₃₂×D₈₉	C₂²	1	2	yes	complemented
38	#508×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	SD₆₄×C₈₉	C₂²	1	2	yes	complemented
41	D₃₂×C₈₉	C₂²	1	2	yes	complemented
42	M₆₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#41×D₈₉	—	4	1	no	—
44	C₂×D₄×D₈₉	—	4	1	no	—
45	#15668035	—	2	1	no	—
46	#15668034	—	2	1	no	—
47	#15668033	—	4	1	no	—
48	#15668032	—	4	1	no	—
49	#15668031	—	2	1	no	—
50	Q₁₆×D₈₉	—	2	1	no	—
51	SD₁₆×D₈₉	—	4	1	no	—
52	C₂×D₇₁₂	—	2	1	no	—
53	C₂×#13083559	—	4	1	no	—
54	D₈×D₈₉	—	2	2	no	—
55	D₈×D₈₉	—	2	2	no	—
56	D₈×D₈₉	—	2	1	no	—
57	D₈×D₈₉	—	4	1	no	—
58	D₈×D₈₉	—	4	1	no	—
59	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
60	Dic₇₁₂	C₂³	1	1	yes	characteristic, complemented
61	#15667958	—	2	1	no	—
62	#15667957	—	2	1	no	—
63	#15667956	—	2	1	no	—
64	#15667955	—	2	1	no	—
65	D₁₄₂₄	—	2	1	no	—
66	D₁₄₂₄	C₂³	1	2	yes	—
67	D₁₄₂₄	C₂³	1	1	yes	characteristic, complemented
68	#15667953	—	2	2	no	—
69	#15667953	—	2	2	no	—
70	#15667953	—	2	1	no	—
71	C₂×#13083549	D₄	1	1	yes	characteristic
72	C₁₆×D₈₉	D₄	1	1	yes	characteristic
73	C₁₆×D₈₉	D₄	1	1	yes	characteristic
74	C₁₆×D₈₉	C₂³	1	1	yes	characteristic
75	C₁₆×D₈₉	C₂³	1	1	yes	characteristic
76	#15667918	C₂³	1	2	yes	complemented
77	#135×C₈₉	—	2	1	no	—
78	C₂×D₈×C₈₉	—	2	1	no	—
79	Q₃₂×C₈₉	C₂³	1	1	yes	characteristic, complemented
80	SD₃₂×C₈₉	—	2	1	no	—
81	D₁₆×C₈₉	—	2	1	no	—
82	D₁₆×C₈₉	C₂³	1	2	yes	—
83	D₁₆×C₈₉	C₂³	1	1	yes	characteristic, complemented
84	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
85	C₃₂×C₈₉	C₂³	1	2	yes	complemented
86	C₂³×D₈₉	—	8	1	no	—
87	#13083575	—	4	1	no	—
88	#13083574	—	4	1	no	—
89	#13083574	—	8	1	no	—
90	#13083573	—	4	1	no	—
91	#13083573	—	8	1	no	—
92	Q₈×D₈₉	—	4	1	no	—
93	C₂×D₃₅₆	—	4	1	no	—
94	C₂×C₂²⋊D₈₉	—	8	1	no	—
95	D₄×D₈₉	—	4	2	no	—
96	D₄×D₈₉	—	4	2	no	—
97	D₄×D₈₉	—	4	1	no	—
98	D₄×D₈₉	—	8	1	no	—
99	D₄×D₈₉	—	8	1	no	—
100	D₄×D₈₉	—	8	1	no	—
101	C₂×C₄×D₈₉	—	8	1	no	—
102	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
103	Dic₃₅₆	—	2	1	no	—
104	#13083564	—	4	1	no	—
105	#13083563	—	4	1	no	—
106	#13083562	—	4	1	no	—
107	#13083561	—	4	1	no	—
108	D₇₁₂	—	2	2	no	—
109	D₇₁₂	—	2	1	no	—
110	D₇₁₂	—	4	1	no	—
111	#13083559	—	4	2	no	—
112	#13083559	—	4	2	no	—
113	#13083559	—	4	1	no	—
114	C₂×#10623494	D₈	1	1	yes	characteristic
115	C₈×D₈₉	D₈	1	1	yes	characteristic
116	C₈×D₈₉	D₈	1	1	yes	characteristic
117	C₈×D₈₉	C₂×D₄	1	1	yes	characteristic
118	C₈×D₈₉	C₂×D₄	1	1	yes	characteristic
119	#13083549	C₂×D₄	1	1	yes	characteristic
120	#13083549	C₂×D₄	1	1	yes	characteristic
121	#41×C₈₉	—	4	1	no	—
122	C₂×D₄×C₈₉	—	4	1	no	—
123	Q₁₆×C₈₉	—	2	1	no	—
124	SD₁₆×C₈₉	—	4	1	no	—
125	D₈×C₈₉	—	2	2	no	—
126	D₈×C₈₉	—	2	1	no	—
127	D₈×C₈₉	—	4	1	no	—
128	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₁₆×C₈₉	C₂⁴	1	1	yes	characteristic
131	C₂³×C₈₉	—	8	1	no	—
132	C₂²×D₈₉	—	8	1	no	—
133	C₂²×D₈₉	—	8	1	no	—
134	C₂²×D₈₉	—	8	2	no	—
135	C₂²×D₈₉	—	8	2	no	—
136	C₂²×D₈₉	—	16	4	no	—
137	C₂²×D₈₉	D₁₆	1	1	yes	characteristic
138	Q₈×C₈₉	—	4	1	no	—
139	D₄×C₈₉	—	4	2	no	—
140	D₄×C₈₉	—	4	1	no	—
141	D₄×C₈₉	—	8	1	no	—
142	D₄×C₈₉	—	8	1	no	—
143	C₂×C₄×C₈₉	—	8	1	no	—
144	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
145	C₂²⋊D₈₉	—	8	1	no	—
146	C₂²⋊D₈₉	—	8	1	no	—
147	C₂²⋊D₈₉	—	8	2	no	—
148	C₂²⋊D₈₉	—	8	2	no	—
149	C₂²⋊D₈₉	—	8	1	no	—
150	C₂×Dic₈₉	—	8	1	no	—
151	C₂×Dic₈₉	D₁₆	1	1	yes	characteristic
152	D₃₅₆	—	4	2	no	—
153	D₃₅₆	—	4	1	no	—
154	D₃₅₆	—	8	1	no	—
155	D₃₅₆	—	8	1	no	—
156	C₄×D₈₉	—	8	1	no	—
157	C₄×D₈₉	—	8	1	no	—
158	C₄×D₈₉	—	8	1	no	—
159	C₄×D₈₉	D₁₆	1	1	yes	characteristic
160	C₄×D₈₉	D₁₆	1	1	yes	characteristic
161	C₄×D₈₉	C₂×D₈	1	1	yes	characteristic
162	C₄×D₈₉	C₂×D₈	1	1	yes	characteristic
163	Dic₁₇₈	—	4	1	no	—
164	Dic₁₇₈	—	8	1	no	—
165	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
166	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	#10623494	C₂×D₈	1	1	yes	characteristic
168	#10623494	C₂×D₈	1	1	yes	characteristic
169	C₂²×C₈₉	—	8	1	no	—
170	C₂²×C₈₉	—	8	2	no	—
171	C₂²×C₈₉	—	16	2	no	—
172	C₂²×C₈₉	C₂×D₁₆	1	1	yes	characteristic
173	C₂×D₈₉	—	2	2	no	—
174	C₂×D₈₉	—	8	1	no	—
175	C₂×D₈₉	—	8	2	no	—
176	C₂×D₈₉	—	16	4	no	—
177	C₂×D₈₉	—	16	2	no	—
178	C₂×D₈₉	—	16	2	no	—
179	C₂×D₈₉	—	16	4	no	—
180	C₂×D₈₉	C₂×D₁₆	1	1	yes	characteristic
181	C₂×D₈₉	C₂×D₁₆	1	1	yes	characteristic
182	C₄×C₈₉	—	8	1	no	—
183	C₄×C₈₉	C₂×D₁₆	1	1	yes	characteristic
184	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
185	Dic₈₉	—	8	1	no	—
186	Dic₈₉	C₂×D₁₆	1	1	yes	characteristic
187	Dic₈₉	C₂×D₁₆	1	1	yes	characteristic
188	C₂×#2263	—	89	1	no	maximal, Sylow
189	C₂×C₈₉	—	2	1	no	—
190	C₂×C₈₉	—	16	2	no	—
191	C₂×C₈₉	—	16	1	no	—
192	C₂×C₈₉	C₂²×D₁₆	1	1	yes	characteristic
193	D₈₉	—	2	1	no	—
194	D₈₉	—	16	1	no	—
195	D₈₉	—	16	2	no	—
196	D₈₉	#2263	1	2	yes	direct product factor
197	C₂×#508	—	89	1	no	—
198	C₂²×D₁₆	—	89	1	no	—
199	#2263	—	89	1	no	—
200	#2263	—	89	1	no	—
201	#2263	—	89	2	no	—
202	#2263	—	89	2	no	—
203	#2263	—	89	1	no	—
204	#2263	D₈₉	1	1	yes	characteristic, direct product factor
205	C₂×SD₆₄	—	89	2	no	—
206	C₂×D₃₂	—	89	2	no	—
207	C₂×M₆₄	—	89	1	no	—
208	C₈₉	C₂×#2263	1	1	yes	characteristic, complemented, Sylow
209	C₂×#135	—	178	1	no	—
210	C₂²×D₈	—	178	1	no	—
211	#508	—	89	1	no	—
212	#508	—	89	1	no	—
213	#508	—	89	1	no	—
214	#508	—	178	1	no	—
215	#508	—	178	1	no	—
216	#508	C₂×D₈₉	1	1	yes	characteristic, complemented
217	C₂×Q₃₂	—	89	1	no	—
218	C₂×SD₃₂	—	178	1	no	—
219	C₂×D₁₆	—	89	2	no	—
220	C₂×D₁₆	—	89	2	no	—
221	C₂×D₁₆	—	89	1	no	—
222	C₂×D₁₆	—	89	1	no	—
223	C₂×D₁₆	—	178	1	no	—
224	C₂×D₁₆	—	178	1	no	—
225	C₂×D₁₆	—	178	1	no	—
226	C₂×D₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
227	C₂²×C₁₆	—	89	1	no	—
228	SD₆₄	—	89	2	no	—
229	SD₆₄	—	89	2	no	—
230	SD₆₄	—	89	2	no	—
231	SD₆₄	C₂×D₈₉	1	2	yes	complemented
232	D₃₂	—	89	2	no	—
233	D₃₂	—	89	2	no	—
234	D₃₂	—	89	2	no	—
235	D₃₂	C₂×D₈₉	1	2	yes	complemented
236	M₆₄	—	89	1	no	—
237	M₆₄	—	89	2	no	—
238	M₆₄	C₂×D₈₉	1	1	yes	characteristic, complemented
239	C₂×C₃₂	—	89	2	no	—
240	C₂×#41	—	356	1	no	—
241	C₂²×D₄	—	356	1	no	—
242	#135	—	2	1	no	—
243	#135	—	356	1	no	—
244	#135	—	356	1	no	—
245	#135	—	178	1	no	—
246	#135	—	178	1	no	—
247	#135	—	178	1	no	—
248	C₂×Q₁₆	—	178	1	no	—
249	C₂×SD₁₆	—	356	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	—	356	1	no	—
252	C₂×D₈	—	356	1	no	—
253	C₂×D₈	—	356	1	no	—
254	C₂×D₈	—	178	2	no	—
255	C₂×D₈	—	178	2	no	—
256	C₂×D₈	—	178	1	no	—
257	C₂×D₈	—	178	1	no	—
258	C₂²×C₈	—	89	1	no	—
259	Q₃₂	—	89	1	no	—
260	Q₃₂	—	178	1	no	—
261	Q₃₂	C₂²×D₈₉	1	1	yes	characteristic, complemented
262	SD₃₂	—	2	1	no	—
263	SD₃₂	—	178	1	no	—
264	SD₃₂	—	178	1	no	—
265	SD₃₂	—	178	1	no	—
266	D₁₆	—	2	1	no	—
267	D₁₆	—	89	1	no	—
268	D₁₆	—	89	2	no	—
269	D₁₆	—	178	2	no	—
270	D₁₆	—	178	2	no	—
271	D₁₆	—	178	1	no	—
272	D₁₆	—	178	1	no	—
273	D₁₆	C₂²×D₈₉	1	2	yes	—
274	D₁₆	C₂²×D₈₉	1	1	yes	characteristic, complemented
275	C₂×C₁₆	—	89	1	no	—
276	C₂×C₁₆	—	89	1	no	—
277	C₂×C₁₆	—	89	1	no	—
278	C₂×C₁₆	—	89	1	no	—
279	C₂×C₁₆	—	89	1	no	—
280	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
281	C₃₂	—	89	2	no	—
282	C₃₂	C₂²×D₈₉	1	2	yes	complemented
283	C₂⁴	—	712	1	no	—
284	#41	—	4	1	no	—
285	#41	—	356	1	no	—
286	#41	—	356	1	no	—
287	#41	—	356	1	no	—
288	#41	—	712	1	no	—
289	#41	—	712	1	no	—
290	C₂×Q₈	—	356	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	356	2	no	—
293	C₂×D₄	—	356	2	no	—
294	C₂×D₄	—	356	1	no	—
295	C₂×D₄	—	356	1	no	—
296	C₂×D₄	—	712	1	no	—
297	C₂×D₄	—	712	1	no	—
298	C₂×D₄	—	712	1	no	—
299	C₂×D₄	—	712	1	no	—
300	C₂²×C₄	—	89	1	no	—
301	C₂²×C₄	—	712	1	no	—
302	Q₁₆	—	2	1	no	—
303	Q₁₆	—	356	1	no	—
304	Q₁₆	—	178	1	no	—
305	SD₁₆	—	4	1	no	—
306	SD₁₆	—	356	1	no	—
307	SD₁₆	—	356	1	no	—
308	SD₁₆	—	356	1	no	—
309	D₈	—	2	2	no	—
310	D₈	—	2	1	no	—
311	D₈	—	4	1	no	—
312	D₈	—	356	2	no	—
313	D₈	—	356	2	no	—
314	D₈	—	356	1	no	—
315	D₈	—	356	1	no	—
316	D₈	—	178	2	no	—
317	D₈	—	178	1	no	—
318	C₂×C₈	—	89	1	no	—
319	C₂×C₈	—	89	1	no	—
320	C₂×C₈	—	89	1	no	—
321	C₂×C₈	—	89	1	no	—
322	C₂×C₈	—	89	1	no	—
323	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
324	C₁₆	—	89	1	no	—
325	C₁₆	—	89	1	no	—
326	C₁₆	D₄×D₈₉	1	1	yes	characteristic
327	C₁₆	C₂³×D₈₉	1	1	yes	characteristic
328	C₂³	—	8	1	no	—
329	C₂³	—	89	1	no	—
330	C₂³	—	1424	4	no	—
331	C₂³	—	712	1	no	—
332	C₂³	—	712	2	no	—
333	C₂³	—	712	2	no	—
334	C₂³	—	712	1	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	356	1	no	—
337	Q₈	—	712	1	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	1	no	—
340	D₄	—	8	1	no	—
341	D₄	—	8	1	no	—
342	D₄	—	356	2	no	—
343	D₄	—	356	1	no	—
344	D₄	—	712	1	no	—
345	D₄	—	712	2	no	—
346	D₄	—	712	2	no	—
347	D₄	—	712	1	no	—
348	D₄	—	712	1	no	—
349	D₄	—	712	1	no	—
350	D₄	—	712	1	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	89	1	no	—
353	C₂×C₄	—	89	1	no	—
354	C₂×C₄	—	89	1	no	—
355	C₂×C₄	—	89	1	no	—
356	C₂×C₄	—	89	1	no	—
357	C₂×C₄	—	712	1	no	—
358	C₂×C₄	—	712	1	no	—
359	C₂×C₄	—	712	1	no	—
360	C₂×C₄	—	712	1	no	—
361	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
362	C₈	—	89	1	no	—
363	C₈	—	89	1	no	—
364	C₈	D₈×D₈₉	1	1	yes	characteristic
365	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
366	C₂²	—	8	1	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	16	2	no	—
369	C₂²	—	89	1	no	—
370	C₂²	—	89	1	no	—
371	C₂²	—	1424	2	no	—
372	C₂²	—	1424	4	no	—
373	C₂²	—	1424	2	no	—
374	C₂²	—	1424	4	no	—
375	C₂²	—	178	2	no	—
376	C₂²	—	712	1	no	—
377	C₂²	—	712	2	no	—
378	C₂²	D₁₆×D₈₉	1	1	yes	characteristic
379	C₄	—	8	1	no	—
380	C₄	—	89	1	no	—
381	C₄	—	89	1	no	—
382	C₄	—	712	1	no	—
383	C₄	D₁₆×D₈₉	1	1	yes	characteristic
384	C₄	C₂×D₈×D₈₉	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	16	2	no	—
387	C₂	—	16	1	no	—
388	C₂	—	89	2	no	—
389	C₂	—	1424	2	no	—
390	C₂	—	1424	1	no	—
391	C₂	—	178	1	no	—
392	C₂	C₂×D₁₆×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₁₆×D₈₉
commutator, cosocle	C₁₆×C₈₉	C₂⁴
Frattini	C₁₆	C₂³×D₈₉
Fitting	C₈₉×#2263	C₂
socle	C₂×C₈₉	C₂²×D₁₆
hypercenter	#2263	D₈₉
hypocenter	C₈₉	C₂×#2263
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #2263

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #508×D₈₉	C₂	semidirect
2. C₂×D₁₆×D₈₉	C₂	semidirect
3. #26022567	C₂	semidirect
4. #26022566	C₂	semidirect
5. #26022565	C₂	semidirect
6. #26022564	C₂	semidirect
7. #26022563	C₂	semidirect
8. SD₆₄×D₈₉	C₂	semidirect
9. D₃₂×D₈₉	C₂	semidirect
10. M₆₄×D₈₉	C₂	semidirect
11. C₈₉×#2263	C₂	semidirect
14. #19152031	C₂²	semidirect
15. #19152030	C₂²	semidirect
18. #19152027	C₂²	semidirect
19. Q₃₂×D₈₉	C₂²	semidirect
21. C₂×D₁₄₂₄	C₂²	semidirect
26. D₁₆×D₈₉	C₂²	semidirect
27. D₁₆×D₈₉	C₂²	semidirect
29. #19151437	C₂²	semidirect
30. #19151436	C₂²	semidirect
31. #19151435	C₂²	semidirect
32. D₂₈₄₈	C₂²	semidirect
33. #19151433	C₂²	semidirect
34. #19151433	C₂²	semidirect
35. #19151432	C₂²	semidirect
36. #19151431	C₂²	semidirect
37. C₃₂×D₈₉	C₂²	semidirect
38. #508×C₈₉	C₂²	semidirect
39. C₂×D₁₆×C₈₉	C₂²	semidirect
40. SD₆₄×C₈₉	C₂²	semidirect
41. D₃₂×C₈₉	C₂²	semidirect
42. M₆₄×C₈₉	C₂²	semidirect
60. Dic₇₁₂	C₂³	semidirect
67. D₁₄₂₄	C₂³	semidirect
76. #15667918	C₂³	semidirect
79. Q₃₂×C₈₉	C₂³	semidirect
83. D₁₆×C₈₉	C₂³	semidirect
85. C₃₂×C₈₉	C₂³	semidirect
196. D₈₉	#2263	direct (N × H)
204. #2263	D₈₉	direct (N × H)
208. C₈₉	C₂×#2263	semidirect
216. #508	C₂×D₈₉	semidirect
226. C₂×D₁₆	C₂×D₈₉	semidirect
231. SD₆₄	C₂×D₈₉	semidirect
235. D₃₂	C₂×D₈₉	semidirect
238. M₆₄	C₂×D₈₉	semidirect
261. Q₃₂	C₂²×D₈₉	semidirect
274. D₁₆	C₂²×D₈₉	semidirect
282. C₃₂	C₂²×D₈₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#508×D₈₉	2
C₂×D₁₆×D₈₉	2
#26022567	2
#26022566	2
#26022565	2
#26022564	2
#26022563	2
SD₆₄×D₈₉	2
D₃₂×D₈₉	2
M₆₄×D₈₉	2
C₈₉×#2263	2
C₂×#2263	89

Subgroups — #2263×D89 #36712558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2263×D₈₉ #36712558